In addition to epic poetry, tragedy, comedy and history, the Greeks pioneer yet another branch of literature - philosophy.

The earliest Greek philosophers, begining with Thales in the 6th century, are concerned chiefly with what we would call science. They seek explanations of the mysteries of the cosmos and of our planet. But their method is philosophical rather than scientific. Instead of observing the natural world, and testing their ideas against what they observe (a scientific procedure for which they lack the equipment), they take a more high-minded and dangerous route. They dream up magnificent theories which can only be judged by their own interior consistency - a congenital habit of philosophers.

The first man to call himself a philosopher (philosophos 'lover of wisdom') is Pythagoras, whose mystical system of mathematics combines some genuine scientific analysis with much other-worldly speculation.

One of the first Greek thinkers to deserve the name of philosopher in its modern sense is believed to have had links with the sect of Pythagoras in southern Italy. He is Parmenides, who concentrates not so much on what reality may be as on what 'being' actually means. This is an undying question for philosophers. In tackling it, in a poem called Nature, Parmenides pioneers one of philosophy's essential tools - the technique of logic, ensuring that a conclusion follows inevitably from a premise.

Philosophy and Athens: 5th century BC

Greece, in the century following Parmenides, sees the rise of a professional class often described as philosophers. They are the Sophists, who derive their name from the same Greek root, sophos. But unlike pure philosophers, their aims are practical. They are travelling teachers, earning their living by educating the sons of the rich.

Education of this kind is carried out largely in conversation. The dialogue becomes a feature of the classroom, and the art of persuasion - formalized as rhetoric - is an important part of the curriculum. Like the teaching of Confucius in China a little earlier, this training prepares young men to make their way in the world. There is a particular need for it in Athens.

Democracy in Athens is more extensively developed than in any other Greek city-state. This means that the ability to persuade others, in a public speech, is more necessary in a political career here than elsewhere. There are rich families willing to buy that skill for their sons, and talented men from less privileged backgrounds eager to acquire it too.

The result is a thriving culture of successful masters with often aristocratic pupils. From it there emerges a brilliant teacher who differs in two important respects from the Sophists. He does not charge for his services, and he regards the pursuit of truth as an end in itself. He is Socrates.

Socrates: late 5th century BC

Socrates, one of the most famous philosophers in history, is the author of not a single book. All that is known about his philosophy derives from what he says in the Socratic dialogues of Plato. These are written some years after his death. It is a much debated question whether the ideas they contain are mainly those of Socrates or Plato.

During his life Socrates is a familiar figure in Athens - sufficiently so to be satirized in 423 BC in a play of Aristophanes, The Clouds (the modern equivalent would be featuring on television in Spitting Image). He is said to be ugly in appearance. He is also eccentric, cussed and tetchy, but with an underlying charm - characteristics shared by many a great teacher.

Socrates spends much of his time in the open air, discussing matters of importance with anyone who wishes to join in. Such meetings often take place in one of the city's gymnasiums - public spaces where young men can train in the various Greek sports.

The regular members of Socrates' circle tend to be rich young men with time on their hands, whose inclinations are against democracy and in favour of oligarchy. An education in logic gives the group a natural scepticism. They regard the traditional Greek gods (a quarrelsome, vindictive and libidinous bunch) as figures of fiction rather than serious objects of devotion. The character of these young aristocrats has a bearing on the death of Socrates.

The trial and death of Socrates: 399 BC

After the defeat of Athens by Sparta in 404 an oligarchic government, brought to power by the Spartans, imposes a brief reign of terror on the city. Democracy is soon restored, but some followers of Socrates have been connected with the repressive oligarchs. In 399 a charge of impiety is brought against him. The two particular accusations are 'corruption of the young' and 'neglect of the gods whom the city worships'.

Plato is in court on the day of the trial. Some years later he writes the Apology, an account of what Socrates says in his own defence. It is in itself partly a Socratic dialogue; the philosopher leads his accuser into various absurd statements.

The Apology (if at all close to what Socrates says on the day of the trial) seems too philosophical for the average jury, let alone an Athenian jury of 500 citizens. Socrates is convicted - but only by a fairly small majority, probably 280 to 220.

The next stage is for prosecutor and defendant each to suggest a punishment. The jury must choose between them. The prosecutor demands death. It seems certain that an almost balanced jury will accept any more reasonable suggestion by Socrates. Instead he declares himself a public benefactor, more deserving of reward than punishment, and proposes a very small fine. The affronted jury votes, by a larger majority than before, for death.

The date of an annual religious event delays the execution for a month, during which Socrates entertains his friends in prison. Escape would be easy, but he rejects it on the grounds that the law must be obeyed.

Execution in Athens is by a relatively civilized method. The condemned man drinks hemlock, a poison which slowly numbs the body. He can be accompanied by his friends. Plato on this occasion is not present. But in the Phaedo he describes the last round of philosophical conversation between Socrates and a circle of followers. The day ends with the drinking of the cup and Socrates' slow death. The only person to remain calm is the victim, 'the most wise and just and best of men'.

Plato: c.428-c.347 BC

Plato's fame today derives from his philosophical works, perhaps more influential than any others over the centuries. In his own time an equally great accomplishment is the school he establishes in about 387 BC in Akademia, a suburb of Athens. From the accident of its location come the words 'academy' and 'academic'.

Instruction at the school includes mathematics (in the mystical tradition of Pythagoras), geometry, law and the natural sciences - in addition to philosophy. Plato's academy lasts more than nine centuries, until closed in AD 529 by the Christian emperor Justinian. It has a good claim to be considered the world's first university.

Plato's books are not directly connected with the academy, but the convention in which they are written must reflect the way in which teaching is carried out. In each so-called Socratic dialogue, named characters progress together in discussion towards some form of agreed conclusion.

This follows a tradition probably established by Socrates himself, who is the central character in most of Plato's works. Four of them, in particular, provide a rounded character portrayal of him. They set out to defend his reputation against the charges which led to his death.

The Euthyphro takes place just before the trial of Socrates. In it he discusses religion with Euthyprho, dealing with the charges laid against him of impiety. The Apology is Plato's eyewitness record of the speech made by Socrates in his own defence to the jury. The Crito takes place in Socrates' prison cell; his friend Crito arrives with the means and the method for him to escape; Socrates persuades him that it would be wrong to do so. And the Phaedo describes Socrates' last day, in which he discusses the soul and immortality before calmly confronting death.

So these dialogues show Socrates, respectively, as devout, persuasive, law-abiding and courageous. They are the tribute of a devotee to a master.

The Symposium and Platonic love

The Symposium, one of the best-known pieces featuring Socrates, is almost an early example of a novella, or short novel. It describes Socrates going as a guest to a dinner held in 416 BC in the house of a playwright, Agathon, who in that year achieves his first theatrical victory in the Lenaea. (The victory and the playwright are historical, but not one of his plays has survived.)

It is decided that each man shall take it in turns to make a speech in praise of Eros, the god of love. Through the sequence of speeches, and the conversation arising from them, Plato is able to turn the occasion into a dialogue on the nature of love.

The love in question is essentially homosexual, which in Athens usually means a relationship between an older and a younger man. In theory the older man, the lover, is inflamed by the beauty of the loved one, while the younger man, the object of love, learns from the greater experience and wisdom of his friend.

One of the main gathering places for social life is the gymnasium, where men train and exercise naked. So the appreciation of male beauty is an everyday fact of life. Since women are largely restricted to the home, relationships between men are the only form of sexual friendship to be seen and acknowledged in public.

The discussion in the Symposium soon reveals such everyday lovers to be merely on the first rung of a ladder of excellence. Like all who love, they are searching for what is good and beautiful; but their satisfaction is mainly physical. Lovers at a higher level are inspired by physical beauty to become intellectually creative. Beyond that, at a stage reached by Socrates and by other good philosophers, physical beauty in this world leads the soul in search of a higher and more absolute beauty.

Somewhere on this ladder of progression physical experience becomes unnecessary. Hence the abiding concept of Platonic love (Socrates fails even to notice the attempt of Alcibiades to seduce him).

The doctrine of Forms and the analogy of the cave

The idea of a higher Beauty or Good (the two are treated as if almost synonymous), of which the reality known to us is only a pale reflection, is a central concept in Plato's philosophy. Known as the theory of Forms, it probably derives from Socrates but is much elaborated by Plato.

The Forms are eternal realities, existing in some higher realm, of which our physical senses only perceive a transient and partial version. There are not only Forms of abstract qualities such as Beauty and Good. There is even, somewhere, the ideal Form of a tree, a chair or a cow.

In his most wide-ranging and ambitious work, the Republic, Plato attempts to explain this concept. He likens the Good, which he sees as the source of all reality, to the sun. They have two main things in common. The sun is a generative force, causing things to exist and grow; so is the Good. More important as an analogy, in terms of Plato's philosophy, is the sun as the source of light. It is light which enables our eyes to have partial sight of reality. In the same way Good enables our minds to have partial knowledge of what is real.

In each case we perceive what is real with varying clarity. To demonstrate this, Plato produces his most famous analogy - that of the cave.

A long deep cave, with a distant opening to the outside world, provides the context in which Plato sets up his different levels of apprehended reality. At first his human observers are prisoners in the cave, seated in a fixed position with their backs to a fire. Their eyes take reality to be the shadows cast by the fire. Then they turn to look towards the fire. After an initial shock they accept the increase in dimension and colour as the real world.

Finally they go out of the cave. Their eyes dazzle. At first they can only look at shadows, then at reflections in water, and finally at what we ourselves take for everyday reality.

For Plato the ordinary man or woman is the prisoner looking at shadows in the cave. The philosopher, who according to the argument of Plato's Republic should also be the ruler in society, undertakes the journey out of the cave towards increasing knowledge of the Good which is absolute reality.

It is a religious concept, whether the ultimate be Good or God. It is echoed in St Paul's famous contrast between this world and the next: 'Now we see through a glass, darkly; but then face to face.' This mystical side of Plato's philosophy, reflected later in Neo-Platonism, has been one reason for the appeal of his work. The other is his brilliance as an author, giving philosophical dialectic the qualities of drama and literature.

Aristotle: 384-322 BC

It is a striking fact that the three greatest philosophers of the ancient world are like three generations of an Athenian family. Socrates, in the last ten years of his life, discusses the eternal verities with Plato, a young member of his circle. Plato, in the last 20 years of his life, has Aristotle as first a pupil and then a teaching colleague in his famous academy. The trio, whose ideas in different ways dominate western speculation for the next two millennia, are in a very real sense akin to a grandfather, father and son.

But while the first two generations remain closely linked, the third - in the form of Aristotle - takes a radically different approach.

Aristotle comes from the peninsula of Chalcidice, in northern Greece, and his family has strong links with neighbouring Macedonia - where his father has been personal physician to the king, Amyntas III. At the age of seventeen Aristotle is sent to Athens, to study at Plato's academy. He remains there for twenty years, until Plato's death in 347 BC.

At this point he leaves Athens. The main reason is no doubt Plato's death, but anti-Macedonian sentiment in the city may have contributed. Greece is increasingly threatened by the expansionist ambitions of Philip II, son of Amyntas III. Aristotle may have felt it wise to move on. And by 343 he is in Philip's employment, as tutor to his son Alexander.

Macedonian control in Greece is established after a congress at Corinth in 337, and in 335 Aristotle returns to Athens. He now sets up his own school in the peripatos or covered walkway of the Lyceum, one of the leading gymnasiums of Athens. Whether he walks while teaching, or merely sits in the walkway, the peripatos becomes so associated with his school that his followers are later known as Peripatetics.

This is probably the point at which his teaching begins to diverge from that of Plato. All his early works are lost, but references to them suggest that they were Socratic dialogues of a kind intended, like Plato's, to make attractive reading. His surviving texts are altogether more severe.

Indeed it has even been suggested that many of Aristotle's texts are his lecture notes, edited by his followers into more readable form. Certainly the tortuous route by which they have reached us is a fascinating example of the haphazard way in which ancient texts survive. It begins in the library of his successor as head of the school - see the Survival of Aristotle's texts.

Whatever the reason, the surviving Aristotle is essentially practical and commonsensical where Plato is poetic and mystical. This has made him fewer friends in recent times. Nevertheless his achievement is astonishing. He sets himself the task of thinking logically about every aspect of human life, subject by subject. The result is encyclopedic.

The range of Aristotle

Even if some are lost, nearly fifty works attributed to Aristotle have come down to us. They fall into several distinct categories.

Of his various works on logic the Prior Analytics has been the most influential, for it introduces the important device of the syllogism. This is a deductive procedure, used in philosophy ever since, which leads from two categorical premises to an implicit conclusion. (From the premises 'All men need to eat' and 'All Greeks are men', the conclusion can be drawn that 'All Greeks need to eat'.)

A lasting interest attaches to the works in which Aristotle attempts to find underlying principles for the everyday experiences of his own society. In the Ethics he sees happiness as the goal of a good life and introduces his principle of the golden mean - defining each virtue as the middle way between two vices (courage, for example, as the firm ground between cowardice and bravado).

The Politics provides useful insights to the systems and prejudices of Aristotle's times, as well as including his own often sensible objections to the utopian society envisaged in Plato's Republic. The Rhetoric analyzes the essential political skill of the classical world, the art of oratory.

The Poetics can be considered in the same category, since it analyzes the material available to Aristotle in his own society. It is, in effect, the world's first treatise of literary criticism.

From his survey of Greek examples, from Homer onwards, he concludes that the aim of poetry is mimesis - 'imitation' of reality. Men are shown as worse than they really are in comedy, better than they are in epic poetry or tragedy. One difference between these two is that epic poetry has no limits of time, whereas the plot of a tragedy should be completed within a day. The good effect of tragedy, Aristotle believes, is the purging (catharsis) of the emotions through the experience of fear and pity.

Another group of Aristotle's works concerns science. Those of most lasting value are the treatises on natural history, where he differs from most Greeks in attempting a scientific observation of the real world (Darwin, in a famous tribute, acknowledges 'old Aristotle' as the first biologist).

By contrast his astronomy (On the Heavens) suffers from the necessary limitations of his time. Much of his Physics is about large issues (the nature of life, the existence of a Prime Mover) which are nowadays more in the realm of philosophy and religion than of science. But his theory of hot and cold, moist and dry, modifying the four elements, plays an important part in the story of alchemy and thus of chemistry.

The works of Aristotle which are most purely philosophical have accidentally provided us with the word 'metaphysics' for the study of basic questions, or first principles, such as the nature of being and knowing. Aristotle's Metaphysics (meaning literally 'after physics') are given that name in early editions only because they feature after his Physics. The word has subsequently been adapted to mean 'beyond' the physical world.

In the Metaphysics Aristotle dismisses Plato's theory of Forms, as an explanation of differing levels of reality. He replaces it with his own system of 'substances' and 'universals'.

The Platonic and Aristotelian heritage

Between them, in an ever-shifting balance, the works of Plato and Aristotle remain the dominant influence on western thought for 2000 years, until the time of Descartes. In 3rd-century Rome Plotinus merges them in Neo-Platonism. During the dark ages of western Europe their works are preserved and commented on by Greek scholars in Constantinople, by Persians (such as Avicenna) and by Arabs and Jews in Spain (Averröes, Maimonides). Such men hand on the tradition until Aristotle is adopted as the patron saint of scholasticism and Plato, in his turn, of the Renaissance.

This is a remarkable result from some sixty years of hard thinking in ancient Athens.